Cardiovascular Engineering and Technology

, Volume 4, Issue 4, pp 520–534 | Cite as

A Simplified Approach for Simultaneous Measurements of Wavefront Velocity and Curvature in the Heart Using Activation Times

  • Nachaat Mazeh
  • David E. Haines
  • Matthew W. Kay
  • Bradley J. Roth
Article

Abstract

The velocity and curvature of a wave front are important factors governing the propagation of electrical activity through cardiac tissue, particularly during heart arrhythmias of clinical importance such as fibrillation. Presently, no simple computational model exists to determine these values simultaneously. The proposed model uses the arrival times at four or five sites to determine the wave front speed (v), direction (θ), and radius of curvature (ROC) (r 0). If the arrival times are measured, then v, θ, and r 0 can be found from differences in arrival times and the distance between these sites. During isotropic conduction, we found good correlation between measured values of the ROC r 0 and the distance from the unipolar stimulus (r = 0.9043 and p < 0.0001). The conduction velocity (m/s) was correlated (r = 0.998, p < 0.0001) using our method (mean = 0.2403, SD = 0.0533) and an empirical method (mean = 0.2352, SD = 0.0560). The model was applied to a condition of anisotropy and a complex case of reentry with a high voltage extra stimulus. Again, results show good correlation between our simplified approach and established methods for multiple wavefront morphologies. In conclusion, insignificant measurement errors were observed between this simplified approach and an approach that was more computationally demanding. Accuracy was maintained when the requirement that ε (ε = b/r 0, ratio of recording site spacing over wave fronts ROC) was between 0.001 and 0.5. The present simplified model can be applied to a variety of clinical conditions to predict behavior of planar, elliptical, and reentrant wave fronts. It may be used to study the genesis and propagation of rotors in human arrhythmias and could lead to rotor mapping using low density endocardial recording electrodes.

Keywords

Cardiac muscle Propagation velocity Wave front curvature Electrode Anisotropy 

Nomenclature

v

Wave front speed

θ

Angle specifying wave front velocity direction

r0

Radius of curvature

b

Recording sites spacing (shortest distance)

ε

Ratio of electrode spacing over radius of curvature

gix

Intracellular conductivity in the x-direction

giy

Intracellular conductivity in the y-direction

gex

Extracellular conductivity in the x-direction

gey

Extracellular conductivity in the y-direction

tn

Activation time at electrode n, where n = 1, 2, 3, or 4

Δtij

Difference of activation times between the ith and jth electrodes

Δτi

Time for wave front to travel segment i

S1S2

Stimulation protocol using stimulus of strength S1 and at a later time stimulus S2

D

Side of square inside the tissue where fibers curve

POI

Point of interest

DF

Distance formula

LS

Line segments method

4E

Our computational method

VF

Ventricular fibrillation

Vm

Membrane potential

Notes

Acknowledgments

This research was funded by the Department of Cardiovascular Medicine at Beaumont Health System, Royal Oak, Michigan. Dr. M. W. Kay received support from the NIH Grant (HL095828). We wish to thank Drs. R. A. Gray and J. M. Rogers for their helpful discussions and insights.

Conflict of interest

None.

Supplementary material

13239_2013_158_MOESM1_ESM.doc (1.3 mb)
Supplementary material 1 (DOC 1283 kb)

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Copyright information

© Biomedical Engineering Society 2013

Authors and Affiliations

  • Nachaat Mazeh
    • 1
  • David E. Haines
    • 2
  • Matthew W. Kay
    • 3
  • Bradley J. Roth
    • 4
  1. 1.Department of Cardiovascular MedicineBeaumont Health SystemRoyal OakUSA
  2. 2.Department of Cardiovascular MedicineOakland University William Beaumont School of MedicineRoyal OakUSA
  3. 3.Department of Electrical and Computer EngineeringGeorge Washington UniversityWashingtonUSA
  4. 4.Department of PhysicsOakland UniversityRochesterUSA

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